What does estoy enojado mean in spanish?

Lets break it down:

Estoy is the 'yo' or 'I' form of estar, which is to be.

Enojada is an adjective, meaning angry or mad.

The first part of 'contigo' (con) means with, and when you add 'tigo' to the end, is means 'with you'.

So put that all together and you get:

'I am angry with you'